Saying Google offers serverless functionality is like saying water is wet. Of course the behemoth has an edge platform.
In the early days of cloud, Google offered quite some nice and advanced application support through their App Engine. That product was later sort of folded into their general compute/cloud product.
Cloud Run is probably as simple as Google could have done, but still makes your developer-life hard since you’ll need to set up IAM policies, configure VPCs etc. Sadly, there are no shortcuts to Google’s Cloud platform, including Edge Compute.
Having said that, the platform is of course complete. Supports many languages and includes all the bells and whistles you might need if you’re an enterprise and have a wishlist of requirements from the product team.